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Homework answers / question archive / An investor can design a risky portfolio based on two shares, A and B

An investor can design a risky portfolio based on two shares, A and B

Finance

An investor can design a risky portfolio based on two shares, A and B. The standard deviation of Share A is 24% while the standard deviation of Share B is 12%. The correlation coefficient between the returns on A and B is -1. The expected return on Share A is 15% while on Share B it is 9%. What is the expected return of the minimum variance portfolio?

a. 

15%

b. 

12%

c. 

11%

d. 

9%

 

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Computation of Expected Return of the Minimum Variance Portfolio:  
Given,    
Standard Deviation of Share A = 24%  
Standard Deviation of Share B = 12%  
Variance of Share A = 0.0576  =24%^2
Variance of Share B = 0.0144  =12%^2
Correlation (r ) =  -1  
Covariance (Cov) -0.0288  =24%*12%*-1
     
Weight of Share A =  0.333333333  =(0.0144-(-0.0288))/(0.0576+0.0144-(2*-0.0288)
Weight of Share B =  0.666666667  =1-0.33333333
So,    
Expected return of Minimum Variance Portfolio =  11.00%  =(0.3333333*15%)+(0.666667*9%)
     

So, the correct option is C "11%".

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